CN108628171B - Improved thrust distribution method for ship dynamic positioning system - Google Patents
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Abstract
The invention discloses an improved thrust distribution method for a ship dynamic positioning system, and belongs to the technical field of ship dynamic positioning control. The basic idea is that, in order to avoid thrust saturation, normalization processing is firstly carried out on the expected thrust with three degrees of freedom, and then amplification processing is carried out according to the capability of a propulsion system; then, the first distribution is carried out by using a direct distribution method, after the direct distribution, the rotation angle of the full-rotation propeller is calculated and whether the full-rotation propeller enters a rotation forbidden domain or not is judged, if the full-rotation propeller enters the rotation forbidden domain, a boundary value adjacent to the rotation angle forbidden domain is used for replacing the rotation angle forbidden domain, and if the full-rotation propeller does not enter the rotation forbidden domain, an original value is reserved; and finally, updating the propeller position matrix, and performing secondary thrust distribution by using a pseudo-inverse algorithm. The invention can better solve the problems of thrust saturation and rotation angle forbidden domain restriction, has good real-time performance and stability, and can improve the positioning capability of the dynamic positioning system. The invention starts from the real-time point of view and comprehensively considers the problems of forbidden angle of the propeller, thrust saturation constraint and the like.
Description
Technical Field
The invention belongs to the technical field of ship dynamic positioning control, and particularly relates to an improved thrust distribution method for a ship dynamic positioning system.
Background
The dynamic positioning system is one of necessary guarantee equipment of deep sea operation equipment (particularly deep sea operation engineering ships working under severe sea conditions for a long time), can safely and effectively help the ships to complete tasks such as position movement, position keeping, target tracking and the like, and plays an important role in the operation process of the ships. The dynamic positioning system is a closed-loop computer control system, and the function of the dynamic positioning system is to utilize a plurality of propellers of a ship to ensure that the ship keeps the position and heading of the ship under the specified operation range and environmental conditions.
The dynamic positioning control system may generally include a navigation guidance system, a high-level controller, a low-level controller, and the like. The navigation guidance system comprises a measuring system, navigation and guidance. The measurement system comprises a position reference system and a sensor system, and has the functions of measuring the position, heading, attitude and environmental forces of the ship relative to a reference point. The navigation module typically obtains the current position of the vessel using a satellite navigation system. The guidance module generates a reference track or positioning point through user input or task requirements, and determines the set position and heading of each control period controller. The high-rise controller comprises a power positioning controller and a thrust distribution unit. The dynamic positioning controller is a three-degree-of-freedom motion controller, and functions to calculate the longitudinal force, the transverse force and the yawing moment required to resist environmental loads and track a desired track. The thrust distribution unit has the basic task of distributing the three-degree-of-freedom expected thrust command output by the power positioning controller to different propellers so as to output thrust with expected magnitude and direction. The low-level controller is a propeller controller, and the function of the low-level controller is to calculate the azimuth angle, the required rotating speed or the screw pitch of the propeller according to the thrust instruction of each propeller.
With the continuous expansion of the application field of dynamic positioning ships, the requirements on ship control performance and control precision are higher and higher, and more attention is paid to the research of the related field. Thrust distribution has become a hot issue in the field of dynamic positioning research. Many scholars are working on the problem of optimal thrust distribution. The pseudo-inverse algorithm, the sequential quadratic programming and the intelligent optimization algorithm are all applied to the solution of the optimal thrust distribution problem. Although the algorithms can effectively solve the problem of thrust distribution, the algorithms still have some defects, and the pseudo-inverse algorithm does not consider the problems of the saturation phenomenon of the thrust of the propeller and the rotation forbidden angle of the propeller; although the prohibition angle and the thrust range of the thruster are considered in the sequence quadratic programming and intelligent optimization algorithm, the calculation steps are complex and cannot meet the real-time requirement of the dynamic positioning system. Although the thrust allocation method of the ship dynamic positioning system based on the artificial fish swarm algorithm, invented by Xia Guo Qing et al, better solves the problem of the azimuth angle constraint of the propeller and improves the optimization speed, the number of iterations and the calculation time are greatly different when the intelligent optimization algorithm allocates different thrust instructions, so that the requirements of the dynamic positioning system on instantaneity and stability cannot be well met. Therefore, the invention provides an improved thrust distribution method combining the control quantity normalization processing, the direct distribution method and the pseudo-inverse method from the viewpoints of real-time performance and stability and more comprehensively considering the thrust saturation constraint and the rotation angle forbidden domain of the propeller. The improved thrust distribution method can effectively solve the problems of thrust saturation, rotation forbidden angle constraint and the like, and the direct distribution and pseudo-inverse algorithm are introduced, so that the optimal thrust distribution method with strong real-time performance is provided. Meanwhile, the algorithm has simple steps, so that the method has good stability.
Disclosure of Invention
The invention aims to provide an improved thrust distribution method for a ship dynamic positioning system, which can meet the real-time requirement of the dynamic positioning system, meet the constraint conditions of the saturation of a propeller and the constraint conditions of a rotation forbidden angle of the system and improve the positioning capability of the system.
The purpose of the invention is realized by the following technical scheme:
the basic idea is to avoid saturation of the thrust of one or several propellers when the desired thrust of three degrees of freedom in the horizontal plane of the vessel is output simultaneously. The desired thrust in three degrees of freedom in the horizontal plane is first normalized. And then determining the magnification times and weight coefficients of the longitudinal force, the transverse force and the yawing moment according to the capacity of the ship propulsion system, and calculating to obtain the actual expected thrust for the ship. And directly distributing the expected thrust after the normalization processing once, and calculating the magnitude and direction of the thrust of each thruster by direct distribution, but at the moment, the forbidden angle constraint between the thrusters is not considered. Therefore, whether the azimuth angle of each propeller enters a rotation prohibition angle range is judged, and if one or more propeller azimuth angles enter a rotation prohibition domain, a constraint boundary value close to the angle is used as the azimuth angle of the propeller; if the propeller does not exceed the maximum propeller angle, the original azimuth angle is kept. After the first thrust direct distribution is completed, the angle variable in the propeller position matrix can be determined, then the pseudo-inverse algorithm is used for carrying out secondary distribution, and finally the actual thrust size and direction of each propeller are obtained.
An improved thrust distribution method for a dynamic positioning system of a ship specifically comprises the following steps:
the first step is as follows: and (3) carrying out normalization processing on the expected thrust command output by the controller:
when the expected thrust of three degrees of freedom in the horizontal plane of the ship or the control voltage corresponding to the expected thrust is simultaneously output, the thrust of one or a plurality of propellers can be saturated. In order to avoid the phenomenon, three expected control voltages in the horizontal plane need to be normalized, and then the normalized amplification factor and the normalized weight coefficient are determined according to the thrust capacity of the ship actually equipped with a propulsion system.
The second step is that: the first allocation is performed using a direct allocation method:
the direct distribution is that the transverse and longitudinal thrust components of each propeller are directly calculated according to the expected thrust instruction after normalization and amplification, and the direct distribution needs to ensure that the resultant force after distribution is the same as that before distribution. Therefore, a formula for direct distribution needs to be constructed according to the layout characteristics of the propellers.
The third step: and (3) calculating the azimuth angle of the full-rotation propeller:
after direct distribution, the rotating azimuth angle of the propeller is calculated according to the transverse and longitudinal thrust components of the full-rotating propeller, and then whether the rotating angle enters the rotating angle forbidden range or not is judged. If the vehicle enters, the azimuth angle of the propeller needs to be corrected.
The fourth step: updating the position matrix of the propeller, and performing secondary distribution by using a pseudo-inverse algorithm:
and updating the angle variable in the propeller position matrix according to the corrected propeller azimuth angle in the third step, then establishing a quadratic optimization objective function, and solving the optimal thrust of the propeller by using a pseudo-inverse algorithm.
In particular, it is possible to use, for example,
the normalization processing formula for the expected control value output by the controller in the first step is as follows:
δd＝UN×ud
in the formula: deltad＝[δ1 δ2 δ3]TIs a normalized expected control voltage vector; delta1The normalized longitudinal control voltage is obtained; delta2Is the normalized transverse control voltage; delta3Is the normalized desired yaw control voltage; u. ofd＝[uX uY uN]TA control voltage corresponding to a desired thrust;
normalized diagonal array UNAs shown in the following formula:
in the formula: u. ofH＝|uX|+|uY|+|uNI is the sum of absolute values of the three-degree-of-freedom control voltage;
the amplification processing formula of the expected control value output by the controller is as follows:
τd＝Λδd
in the formula: tau isd＝[Xd Yd Nd]TDesired thrust allocation in three degrees of freedom; Λ is the amplification and weight diagonal matrix, which can be represented by:
Λ＝diag{k1l1,k2l2,k3l3}
in the formula: k is a radical of1、k2、k3The magnification times corresponding to longitudinal thrust, transverse thrust and yaw moment are respectively; l1、l2、l3The weight coefficients corresponding to the longitudinal thrust, the transverse thrust and the yaw moment are respectively.
The formula of the direct distribution method in the second step is as follows:
T1＝T2＝59Yd/226.1+Nd/244.1
T3＝0
T4x＝Xd/2+Nd/244.1；
T4y＝54.05Yd/226.1-Nd/244.1
T5x＝Xd/2-Nd/244.1
T5y＝54.5Yd/226.1-Nd/244.1
in the formula: t isi(i ═ 1,2,3,4,5) is the thrust magnitude of each propeller, Tix(i ═ 1,2,3,4,5) denotes the component of the thrust generated by each propeller in the longitudinal direction, Tiy(i ═ 1,2,3,4,5) denotes the component in the transverse direction of the thrust generated by each propeller;
Xd＝T3cosα3+T4cosα4+T5cosα5
Yd＝T1+T2+T3sinα3+T4sinα4+T5sinα5
Nd＝T1l1x+T2l2x+T3yl3x+T4yl4x-T4xl4y-T5yl5x-T5xl5y
wherein alpha isiAnd (i is 3,4,5) represents an included angle between the thrust direction of the full-rotation propeller and the positive direction of the longitudinal axis of the ship, and the instantaneous direction is positive.
The third step is that the calculation formula of the azimuth angle of the full-rotation propeller is as follows:
calculating azimuth angles theta of No. 4 propeller and No. 5 propeller according to the distributed thrusts4And theta5：
The formula for correcting the rotating azimuth angle of the rotating propeller is specifically as follows:
the fourth step of performing secondary distribution by using a pseudo-inverse algorithm specifically comprises the following steps:
the thrust T ═ T actually generated by each propeller1,T2,T3,T4,T5]T：
T＝[T1,T2,T3,T4,T5]T＝W-1BT(BW-1BT)-1τ，
In the formula: w is a positive definite weight matrix; b is a propeller vector arrangement matrix; and tau is a resultant force command output by the controller.
The invention has the beneficial effects that:
the method can quickly and effectively distribute the expected thrust instruction output by the controller to each propeller, can meet the real-time requirement of the dynamic positioning system, meets the constraint conditions of the saturation of the propellers and the constraint conditions of the rotation forbidden angle of the system, and improves the positioning capability of the system.
Drawings
Fig. 1 is a layout diagram of a target ship propeller ( numbers 1,2,3,4 and 5 in the figure represent propellers No. 1,2,3,4 and 5 respectively);
FIG. 2 is a flow chart of the operation of the dynamic positioning system;
FIG. 3 is a block diagram of overdrive thrust distribution and thrust integration;
FIG. 4 shows the installation position and angle of the target vessel;
fig. 5 shows the forbidden zones and thrust ranges of the thruster.
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings:
firstly, establishing a simulation block diagram of target ship motion control and thrust distribution in Matlab software according to the diagram of FIG. 2, and establishing a complete framework of a dynamic positioning simulation system. The method comprises the following steps: the system comprises a target ship hydrodynamics module, a target ship dead reckoning module, a three-degree-of-freedom motion controller, an overdrive thrust distribution module and a thrust synthesis module, wherein the internal principles of the overdrive thrust distribution module and the overdrive thrust synthesis module are described in detail in fig. 3. Since this embodiment is to realize such an improved thrust distribution method, the effect of environmental forces on the vessel is not taken into consideration. The operation of the entire dynamic positioning system and the implementation of the thrust distribution process will be described in detail below.
And secondly, outputting the motion acceleration of the ship under the body coordinate system through the combined external force acting on the ship and the last motion speed by the hydrodynamic module of the target ship. The related hydrodynamic formula is as follows:
in the formula: m is belonged to R3×3Is a ship system inertia matrix; c (. nu.) belongs to R3×3Is a Coriolis centripetal force matrix; d (. nu.) belongs to R3×3A damping force matrix caused by hydrodynamic force; u v ═ u v r]TThe vector of the ship speed and the angular speed under a ship body coordinate system is shown, wherein u is a longitudinal speed, v is a transverse speed, and r is a yawing angular speed;
the ship acceleration and the angular acceleration under a ship body coordinate system are obtained; τ ═ X Y N]TThe combined external force X acting on the ship is a longitudinal force, Y is a transverse force, and N is a bow turning moment. The coefficient matrices M, C (upsilon), D (upsilon) in the hydrodynamic model may be calculated by model experiments or by software related to fluid mechanics.
And thirdly, calculating the acceleration of longitudinal and transverse motions of the ship and the angular acceleration of rotation around the z axis through a hydrodynamics module. The angular velocities in the three directions are converted into a northeast coordinate system through a rotation matrix, and then integration is carried out to obtain the velocity and coordinate position of the ship in the northeast coordinate system. The specific formula is as follows:
in the formula: eta is the position of the ship in a northeast coordinate system; eta0The initial position of the ship in a northeast coordinate system;
the moving speed of the ship in a northeast coordinate system;
the initial speed of the ship in a northeast coordinate system;
the motion acceleration of the ship in a northeast coordinate system; j (ψ) is a rotation matrix for conversion between the northeast coordinate system and the hull coordinate system, where ψ represents the heading angle of the ship.
Fourthly, calculating the resultant external force required by the ship to reach the expected point by utilizing the PID control principle according to the current position of the ship calculated in the previous step and the expected position input by the user, wherein the resultant external force is expressed in a voltage form, namely ud＝[uX uY uN]TWherein u isXDenotes the longitudinal voltage uYRepresents the transverse voltage uNIndicating the heading voltage.
A fifth step, in which the desired thrust generated by the PID controller is represented in the form of a voltage, and the normalized desired control voltage is represented by the following equation:
δd＝UN×ud (4)
in the formula: deltad＝[δ1 δ2 δ3]TIs a normalized expected control voltage vector; delta1The normalized longitudinal control voltage is obtained; delta2Is the normalized transverse control voltage; delta3Is the normalized desired yaw control voltage; u. ofd＝[uX uY uN]TA control voltage corresponding to a desired thrust;
normalized diagonal array UNAs shown in the following formula:
in the formula: u. ofH＝|uX|+|uY|+|uNAnd | is the sum of the absolute values of the three-degree-of-freedom control voltages.
The amplified expression of the normalized desired thrust is:
τd＝Λδd (6)
in the formula: tau isd＝[Xd Yd Nd]TDesired thrust allocation in three degrees of freedom; Λ is the amplification and weight diagonal matrix, which can be represented by:
Λ＝diag{k1l1，k2l2，k3l3} (7)
in the formula: k is a radical of1、k2、k3The magnification times corresponding to longitudinal thrust, transverse thrust and yaw moment are respectively; l1、l2、l3The weight coefficients corresponding to the longitudinal thrust, the transverse thrust and the yaw moment are respectively.
Sixthly, distributing the expected thrust after normalization and amplification
(1) First allocation using direct allocation method
According to the homeNormalized amplified resultant force command τd＝[Xd，Yd，Nd]And the transverse force and the longitudinal force components of each propeller are directly calculated, and direct distribution needs to ensure that the distributed resultant force is consistent with an expected resultant force instruction of the controller. Namely, the following formula is satisfied:
in the formula: t isi(i ═ 1,2,3,4,5) is the thrust magnitude of each propeller, Tix(i ═ 1,2,3,4,5) denotes the component of the thrust generated by each propeller in the longitudinal direction, Tiy(i ═ 1,2,3,4,5) denotes the component in the transverse direction of the thrust generated by each propeller; alpha is alphaiAnd (i is 3,4,5) represents an included angle between the thrust direction of the full-rotation propeller and the positive direction of the longitudinal axis of the ship, and the instantaneous direction is positive. And has Tix＝Ticosαi，Tiy＝Tisinαi。
According to the above principle, and in combination with practical experience, it is assumed that the lateral and longitudinal thrusts of the thruster have the following form, and in order to ensure a good redundancy of the system, the thrust of the thruster No. 3 is made zero when directly allocated.
The direct thrust distribution formula constructed finally is as follows;
T1＝T2＝59Yd/226.1+Nd/244.1
T3＝0
T4x＝Xd/2+Nd/244.1；
T4y＝54.05Yd/226.1-Nd/244.1
T5x＝Xd/2-Nd/244.1
T5y＝54.5Yd/226.1-Nd/244.1
(9)
(2) full-circle-of-rotation propeller azimuth judgment
Calculating No. 4 and No. 5 pushes according to the distributed push forceAzimuth angle theta of the propeller4And theta5。
And then judging whether the azimuth angle of the entering forbidden domain appears in the forbidden domain of the revolution angle, and replacing the azimuth angle of the entering forbidden domain with a forbidden domain boundary value close to the azimuth angle of the entering forbidden domain. If not, the original value is reserved.
(3) And updating the position matrix B of the propeller, and solving for the second time by using a pseudo-inverse algorithm.
The invention is an improved pseudo-inverse algorithm, so that the selected thrust distribution model is a quadratic unconstrained thrust distribution model.
s.t.τ-Bu＝0 (14)
In the formula: w is a positive definite weight matrix; b is a propeller vector arrangement matrix; f is a power function of the propeller; tau is a resultant force instruction output by the controller; u is a thrust instruction output by each thruster;
the propeller system vector arrangement matrix B is shown below; since the azimuth angle theta of the propeller and the direction angle alpha of the thrust are equal in magnitude, only the corresponding theta is needediSubstitution of alphai(i is 3,4, 5).
In the formula: c represents cos (-); s represents sin (·); lix(i is 1,2,3,4,5) is the arm of the longitudinal force of each propeller; liyAnd (i is 1,2,3,4 and 5) is the arm of the transverse force of each propeller.
The thrust T ═ T actually generated by each propeller is calculated according to the following formula1,T2,T3,T4,T5]T：
T＝[T1,T2,T3,T4,T5]T＝W-1BT(BW-1BT)-1τ (16)
Seventhly, distributing the thrust T1,T2,T3,T4,T5Synthesized and then input into a hydrodynamic model of the vessel, thereby driving the vessel to move to a desired position.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. An improved thrust force distribution method for a dynamic positioning system of a ship, characterized by comprising the following steps:
the first step is as follows: and (3) carrying out normalization processing on the expected thrust command output by the controller:
normalizing the three expected control voltages in the horizontal plane, and determining the normalized amplification factor and weight coefficient according to the thrust capability of the actually-equipped propulsion system of the ship;
the second step is that: the first allocation is performed using a direct allocation method:
according to the expected thrust instruction after normalization and amplification, the transverse and longitudinal thrust components of each propeller are directly calculated, and the resultant force after direct distribution is the same as that before distribution;
the third step: and (3) calculating the azimuth angle of the full-rotation propeller:
after direct distribution, calculating the rotation azimuth angle of the propeller according to the transverse and longitudinal thrust components of the full-rotation propeller, then judging whether the rotation angle enters the rotation angle forbidden domain range, and if so, correcting the azimuth angle of the propeller;
the fourth step: updating the position matrix of the propeller, and performing secondary distribution by using a pseudo-inverse algorithm:
and updating the angle variable in the propeller position matrix according to the corrected propeller azimuth angle in the third step, then establishing a quadratic optimization objective function, and solving the optimal thrust of the propeller by using a pseudo-inverse algorithm.
2. The improved thrust force distribution method for the dynamic positioning system of the ship as claimed in claim 1, wherein the normalization processing formula of the expected control value output by the controller in the first step is:
δd＝UN×ud
in the formula: deltad＝[δ1 δ2 δ3]TIs a normalized expected control voltage vector; delta1The normalized longitudinal control voltage is obtained; delta2Is the normalized transverse control voltage; delta3Is the normalized desired yaw control voltage; u. ofd＝[uX uY uN]TA control voltage corresponding to a desired thrust;
normalized diagonal array UNAs shown in the following formula:
in the formula: u. ofH＝|uX|+|uY|+|uNI is the sum of absolute values of the three-degree-of-freedom control voltage; u. ofXIndicates the longitudinal directionVoltage uYRepresents the transverse voltage uNIndicating a heading voltage;
the amplification processing formula of the expected control value output by the controller is as follows:
τd＝Λδd
in the formula: tau isd＝[Xd Yd Nd]TDesired thrust distribution in three degrees of freedom, XdTo expect longitudinal thrust, YdTo expect lateral thrust, NdA desired heading moment; Λ is the amplification and weight diagonal matrix, which can be represented by:
Λ＝diag{k1l1,k2l2,k3l3}
in the formula: k is a radical of1、k2、k3The magnification times corresponding to longitudinal thrust, transverse thrust and yaw moment are respectively; l1、l2、l3The weight coefficients corresponding to the longitudinal thrust, the transverse thrust and the yaw moment are respectively.
3. The improved thrust force distribution method for a dynamic positioning system of a ship as claimed in claim 2, wherein the direct distribution method in the second step has the formula:
T1＝T2＝59Yd/226.1+Nd/244.1
T3＝0
T4x＝Xd/2+Nd/244.1；
T4y＝54.05Yd/226.1-Nd/244.1
T5x＝Xd/2-Nd/244.1
T5y＝54.5Yd/226.1-Nd/244.1
in the formula: t isiWhere i is 1,2,3,4,5 is the thrust magnitude of each propeller, TixWhere i ═ 1,2,3,4,5 denotes the component of the thrust generated by each propeller in the longitudinal direction, TiyWhere i ═ 1,2,3,4,5 denotes the component in the transverse direction of the thrust generated by each propeller;
Xd＝T3cosα3+T4cosα4+T5cosα5
Yd＝T1+T2+T3sinα3+T4sinα4+T5sinα5
Nd＝T1l1x+T2l2x+T3yl3x+T4yl4x-T4xl4y-T5yl5x-T5xl5y
wherein alpha isiWhere i-3, 4,5 denotes the angle between the thrust direction of the full-circle propeller and the forward direction of the longitudinal axis of the vessel, the instantaneous angle being positive, lixWherein i is 1,2,3,4,5 represents TiTo obybHorizontal distance of the shaft; liyWherein i is 1,2,3,4,5 represents TiTo obxbHorizontal distance of the axis.
4. The improved thrust force distribution method for the dynamic positioning system of the ship as claimed in claim 3, wherein the third step is to calculate the azimuth angle of the full-circle-turning propeller according to the following formula:
calculating azimuth angles theta of No. 4 propeller and No. 5 propeller according to the distributed thrusts4And theta5：
The formula for correcting the rotating azimuth angle of the rotating propeller is specifically as follows:
5. the improved thrust force distribution method for a dynamic positioning system of a marine vessel as claimed in claim 4,
the fourth step of performing secondary distribution by using a pseudo-inverse algorithm specifically comprises the following steps:
the thrust T ═ T actually generated by each propeller1,T2,T3,T4,T5]T：
T＝[T1,T2,T3,T4,T5]T＝W-1BT(BW-1BT)-1τ，
In the formula: w is a positive definite weight matrix; b is a propeller vector arrangement matrix; and tau is a resultant force command output by the controller.
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